Question 1

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that q and w are positive numbers. $\log _ { 2 } \frac { q w } { 4 }$

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Question 2

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that w , r , t and a are positive numbers, and $a \neq 1$ . $\log _ { a } \frac { \sqrt [ 5 ] { w } } { \sqrt [ 3 ] { r t } }$

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Question 3

If $\log _ { b } 32 x = 5 + \log _ { b } x$ , find b .

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Question 4

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that w and r are positive numbers. $\log w ^ { 6 } r ^ { 7 }$

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Question 5

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that u , i and p are positive numbers. $\log \text { uip }$

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Question 6

Use the change-of-base formula to find the logarithm to four decimal places. $\log _ { 5 } 9$

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Question 7

Assume that $\log _ { 5 } 9$ , $\log _ { b } 7 = 0.8451$ and $\log _ { b } 9 = 0.9542$ . Use these values to evaluate the logarithm. $\log _ { b } 63$

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Question 8

Solve: $\log x + \log ( x - 15 ) = 2$

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Question 9

Does ${ } ^ { 227 } \mathrm { Th }$ ?

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Question 10

The half-life of tritium is 12.4 years. How long will it take for 25% of a sample of tritium to decompose?
 Please round the answer to the nearest tenth. __________ years

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Question 11

Solve: $3 ^ { 3 x - 3 } = 729$

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Question 12

An equation with a logarithmic expression that contains a variable, such as $\log _ { 5 } ( 2 x - 7 ) = \log _ { 5 } ( x + 1 )$ , is a(n) __________ equation.

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Question 13

Solve each equation. ${ } ^ { 227 } \mathrm { Th }$

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Question 14

Solve the equation. Round answer to four decimal places. $5 ^ { x } = 9$

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Question 15

Solve: $\log _ { 3 } ( x - 5 ) + \log _ { 3 } ( x + 3 ) = \log _ { 3 } 20$

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Question 16

If $500 is deposited in an account paying 8.3% annual interest, compounded semiannually, how long will it take for the account to increase to $850?
 Please round the answer to the nearest tenth. __________ years

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Question 17

Solve the equation. ${ } ^ { 227 } \mathrm { Th }$

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Question 18

If $\log _ { b } x ^ { 2 } = 1 + \log _ { b } 6$ , find b .

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Question 19

Solve: $\log ( x + 5 ) - \log ( x - 2 ) = \log 6$

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Question 20

To solve $7 ^ { x } = 3$ , we can take the _________ of both sides of the equation to get $\log 7 ^ { x } = \log 3$ .

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Quiz 9: Exponential and Logarithmic Functions

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that q and w are positive numbers. log⁡2qw4\log _ { 2 } \frac { q w } { 4 }log2​4qw​

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that w , r , t and a are positive numbers, and a≠1a \neq 1a=1 . log⁡aw5rt3\log _ { a } \frac { \sqrt [ 5 ] { w } } { \sqrt [ 3 ] { r t } }loga​3rt​5w​​

If log⁡b32x=5+log⁡bx\log _ { b } 32 x = 5 + \log _ { b } xlogb​32x=5+logb​x , find b .

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that w and r are positive numbers. log⁡w6r7\log w ^ { 6 } r ^ { 7 }logw6r7

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that u , i and p are positive numbers. log⁡ uip \log \text { uip }log uip

Use the change-of-base formula to find the logarithm to four decimal places. log⁡59\log _ { 5 } 9log5​9

Assume that log⁡59\log _ { 5 } 9log5​9 , log⁡b7=0.8451\log _ { b } 7 = 0.8451logb​7=0.8451 and log⁡b9=0.9542\log _ { b } 9 = 0.9542logb​9=0.9542 . Use these values to evaluate the logarithm. log⁡b63\log _ { b } 63logb​63

Solve: log⁡x+log⁡(x−15) =2\log x + \log ( x - 15 ) = 2logx+log(x−15) =2

Does 227Th{ } ^ { 227 } \mathrm { Th }227Th ?

The half-life of tritium is 12.4 years. How long will it take for 25% of a sample of tritium to decompose? Please round the answer to the nearest tenth. __________ years

Solve: 33x−3=7293 ^ { 3 x - 3 } = 72933x−3=729

An equation with a logarithmic expression that contains a variable, such as log⁡5(2x−7)=log⁡5(x+1)\log _ { 5 } ( 2 x - 7 ) = \log _ { 5 } ( x + 1 )log5​(2x−7)=log5​(x+1) , is a(n) __________ equation.

Solve each equation. 227Th{ } ^ { 227 } \mathrm { Th }227Th

Solve the equation. Round answer to four decimal places. 5x=95 ^ { x } = 95x=9

Solve: log⁡3(x−5) +log⁡3(x+3) =log⁡320\log _ { 3 } ( x - 5 ) + \log _ { 3 } ( x + 3 ) = \log _ { 3 } 20log3​(x−5) +log3​(x+3) =log3​20

If $500 is deposited in an account paying 8.3% annual interest, compounded semiannually, how long will it take for the account to increase to $850? Please round the answer to the nearest tenth. __________ years

Solve the equation. 227Th{ } ^ { 227 } \mathrm { Th }227Th

If log⁡bx2=1+log⁡b6\log _ { b } x ^ { 2 } = 1 + \log _ { b } 6logb​x2=1+logb​6 , find b .

Solve: log⁡(x+5) −log⁡(x−2) =log⁡6\log ( x + 5 ) - \log ( x - 2 ) = \log 6log(x+5) −log(x−2) =log6

To solve 7x=37 ^ { x } = 37x=3 , we can take the _________ of both sides of the equation to get log⁡7x=log⁡3\log 7 ^ { x } = \log 3log7x=log3 .

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that q and w are positive numbers. $\log _ { 2 } \frac { q w } { 4 }$

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that w , r , t and a are positive numbers, and $a \neq 1$ . $\log _ { a } \frac { \sqrt [ 5 ] { w } } { \sqrt [ 3 ] { r t } }$

If $\log _ { b } 32 x = 5 + \log _ { b } x$ , find b .

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that w and r are positive numbers. $\log w ^ { 6 } r ^ { 7 }$

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that u , i and p are positive numbers. $\log \text { uip }$

Use the change-of-base formula to find the logarithm to four decimal places. $\log _ { 5 } 9$

Assume that $\log _ { 5 } 9$ , $\log _ { b } 7 = 0.8451$ and $\log _ { b } 9 = 0.9542$ . Use these values to evaluate the logarithm. $\log _ { b } 63$

Solve: $\log x + \log ( x - 15 ) = 2$

Does ${ } ^ { 227 } \mathrm { Th }$ ?

Solve: $3 ^ { 3 x - 3 } = 729$

An equation with a logarithmic expression that contains a variable, such as $\log _ { 5 } ( 2 x - 7 ) = \log _ { 5 } ( x + 1 )$ , is a(n) __________ equation.

Solve each equation. ${ } ^ { 227 } \mathrm { Th }$

Solve the equation. Round answer to four decimal places. $5 ^ { x } = 9$

Solve: $\log _ { 3 } ( x - 5 ) + \log _ { 3 } ( x + 3 ) = \log _ { 3 } 20$

Solve the equation. ${ } ^ { 227 } \mathrm { Th }$

If $\log _ { b } x ^ { 2 } = 1 + \log _ { b } 6$ , find b .

Solve: $\log ( x + 5 ) - \log ( x - 2 ) = \log 6$

To solve $7 ^ { x } = 3$ , we can take the _________ of both sides of the equation to get $\log 7 ^ { x } = \log 3$ .